The Fermion Dynamic Symmetry Model: Working group report

A new and simple algorithm is presented to solve the fermion dynamical symmetry model numerically in the heritage-zero subspace for neutron-proton systems. The algorithm is based on a shell-model approach using the fermion pair operators as building blocks for the many-body wave functions. The same algorithm applies to all possible neutron and proton Hamiltonians. The results of all known dynamical symmetries are reproduced. Typical approximate vibrational and rotational spectra are presented for cases where dynamical symmetries cannot be found from group chain decompositions.A new and simple algorithm is presented to solve the fermion dynamical symmetry model numerically in the heritage-zero subspace for neutron-proton systems. The algorithm is based on a shell-model approach using the fermion pair operators as building blocks for the many-body wave functions. The same algorithm applies to all possible neutron and proton Hamiltonians. The results of all known dynamical symmetries are reproduced. Typical approximate vibrational and rotational spectra are presented for cases where dynamical symmetries cannot be found from group chain decompositions.

Physical Review CMar 1, 198911 citations

Fermion dynamical-symmetrical model and its boson mapping

K. Baktybaev, N.O. Kojlyk, K.E. Ramankulov

Jan 1, 20060 citations

Eliminating fermionic matter fields in lattice gauge theories

Erez Zohar, J. I. Cirac

We devise a unitary transformation that replaces the fermionic degrees of freedom of lattice gauge theories by (hard-core) bosonic ones. The resulting theory is local and gauge invariant, with the same symmetry group. The method works in any spatial dimension and can be directly applied, among others, to the gauge groups $G=U(N)$ and $SU(2N)$ , where $N\ensuremath{\in}\mathbb{N}$. For $SU(2N+1)$ , one can also carry out the transformation after introducing an extra idle ${\mathbb{Z}}_{2}$ gauge field, so that the resulting symmetry group trivially contains ${\mathbb{Z}}_{2}$ as a normal subgroup. Those results have implications in the field of quantum simulations of high-energy physics models.We devise a unitary transformation that replaces the fermionic degrees of freedom of lattice gauge theories by (hard-core) bosonic ones. The resulting theory is local and gauge invariant, with the same symmetry group. The method works in any spatial dimension and can be directly applied, among others, to the gauge groups $G=U(N)$ and $SU(2N)$, where $N\ensuremath{\in}\mathbb{N}$. For $SU(2N+1)$, one can also carry out the transformation after introducing an extra idle ${\mathbb{Z}}_{2}$ gauge field, so that the resulting symmetry group trivially contains ${\mathbb{Z}}_{2}$ as a normal subgroup. Those results have implications in the field of quantum simulations of high-energy physics models.

arXiv:1805.05347Physical review. B./Physical review. BAug 9, 201874 citations

Hidden symmetry of free Fermion model

Vladimir V. Bazhanov, Yu. G. Stroganov

Theoretical and Mathematical PhysicsMar 1, 198584 citations

Partial dynamical symmetry in an interacting fermion system

Jutta Escher

Czechoslovak Journal of PhysicsJan 1, 20010 citations

Non-Fermi liquid induced by U(1) gauge-field interactions: A functional renormalization group analysis

Thomas P. Sheerin, C. Hooley

We study the non-Fermi-liquid state formed by an isotropic, degenerate Fermi gas in two spatial dimensions interacting with a U(1) gauge field. Our calculation uses the functional renormalization group (fRG) with a soft frequency cutoff for the fermions. The fRG scheme we employ takes account of the gauge symmetry, which imposes relations (modified Ward-Takahashi identities) between the couplings which constrain the RG flow. The critical exponents and couplings we find for the resulting non-Fermi liquid are mostly insensitive to whether we enforce the gauge symmetry constraints, which signifies either that the constraints are superfluous or that the frequency-cutoff scheme is particularly robust. The exception is the gauge-boson mass term, which is RG-relevant about the fixed point without the constraints but is irrelevant when they are enforced. The latter is physically accurate, as a gauge symmetry cannot be spontaneously broken. In addition, we find z = 2 and Σ ( ω , k F ) ∼ ω 1 / 2 for the boson dynamical exponent and scaling of the fermion self-energy, respectively. These results differ considerably from those of past works on the model, though we argue for their plausibility.We study the non-Fermi-liquid state formed by an isotropic, degenerate Fermi gas in two spatial dimensions interacting with a U(1) gauge field. Our calculation uses the functional renormalization group (fRG) with a soft frequency cutoff for the fermions. The fRG scheme we employ takes account of the gauge symmetry, which imposes relations (modified Ward-Takahashi identities) between the couplings which constrain the RG flow. The critical exponents and couplings we find for the resulting non-Fermi liquid are mostly insensitive to whether we enforce the gauge symmetry constraints, which signifies either that the constraints are superfluous or that the frequency-cutoff scheme is particularly robust. The exception is the gauge-boson mass term, which is RG-relevant about the fixed point without the constraints but is irrelevant when they are enforced. The latter is physically accurate, as a gauge symmetry cannot be spontaneously broken. In addition, we find z = 2 and Σ ( ω , k F ) ∼ ω 1 / 2 for the boson dynamical exponent and scaling of the fermion self-energy, respectively. These results differ considerably from those of past works on the model, though we argue for their plausibility.

arXiv:2411.18245Physical Review ResearchJun 2, 20251 citation

G=U(N)

and

SU(2N)

, where $N\ensuremath{\in}\mathbb{N}$. For

SU(2N+1)

, one can also carry out the transformation after introducing an extra idle

{\mathbb{Z}}_{2}

gauge field, so that the resulting symmetry group trivially contains

{\mathbb{Z}}_{2}

as a normal subgroup. Those results have implications in the field of quantum simulations of high-energy physics models.